Sunday, January 13, 2013

The Anthropocentric Foundation of Physics and Mathematics


The Anthropocentric Foundation of Physics and Mathematics

Physics is currently built on an unsound foundation, because it is based on mathematics. Mathematics, as currently defined, is an extended deductive logic system based on a false premise relative to physical existence. Let me explain.

The "unreasonable effectiveness of mathematics in the natural sciences" exists because mathematical structure is a homomorph of the quantum field structure of physical existence. That makes mathematics a very useful tool because we can use it to model parts of many physical systems, and partially predict the outcome of many experiments. The problem is mathematics is only a homomorph of the quantum field structure. It only provides a partial, incomplete, inconsistent, uncertain representation of the observable parts of existence. It is not an isomorph of the totality of physical existence. In less technical terms, that means mathematics does not provide a one-to-one representation of all of physical existence.

Mathematics is not isomorphic to physical existence because the natural numbers are based on the transfinite recursive composition of empty sets. The empty set is an indirect representation of nonexistence. The empty set is an isomorph of, and the logical model for, the number zero (0). In other words, there exists a one-to-one mapping between the empty set and zero, and between zero and nonexistence. The problem is there is no such thing as nonexistence in existence. Nonexistence is the logical complement of existence. It is the complete absence of existence.

Existence cannot represent its own complement, or it would be inconsistent, because it wouldn't be itself. Furthermore, and this is extremely important:

EVERYTHING THAT EXISTS IN THE UNIVERSE IS COMPOSED OF ENERGY

No particle is fundamental. All particles are composed of energy. In this case, I am using the term energy in its broadest possible scope, to include all types of energy, not just the observable kinds. In other words, by the term energy, I mean all types of quantized energy, all types of quantized dark energy, all types of virtual energy, all types of dark virtual energy, the quantum vacuum, and the singularity. Each different type of 'particle' is actually a localized quantum energy field composition with a specific type of quantum field configuration. Its quantum field composition and configuration gives each particle the properties we associate with particles.

The totality of energy in the universe (of all types combined) is a conserved quantity. It is impossible to destroy any energy, let alone all of it. Energy can be transformed from one form to another, including between forms that are observable and unobservable, but none of it can ever be destroyed. In metaphysical terms energy is the arche. In philosophical terms, it is the fundamental 'substance' that composes existence.

Since everything in the universe is composed of energy, that means zero energy, and thus nonexistence, is not part of the universe. Nonexistence is an inconsistent concept relative to physical existence. Even if we remove every particle from a region of space, and cool it down to absolute zero temperature, and shield it from all external energy fields, the resulting vacuum is still full of virtual energy and virtual dark energy. It still contains the quantum vacuum energy. Spacetime itself is composed of energy. There is simply no way to remove all energy from anyplace, let alone destroy all energy in the universe. Where would it go, universe 2? There is no such thing. The universe is everything that exists. There can only be one everything. Since the empty set is an isomorph of nonexistence, the empty set, and by extension the concept of zero, is also not part of physical existence, and is thus inconsistent with physical existence.

It is also easy to see this from the perspective of special relativity. Zero is the  origin of the number system. Yet what is the absolute origin of physical existence? Where is zero in space? When is zero in time? Time and space are both relative. They have no absolute origin. They are relative because they are both composed of energy, and energy is a substance that differences can occur in. In particular, those differences are what causes the existence of potential differences in energy fields, the differences between states, the quantization of energy, and thus the existence of quantized energy fields, quantum states, and finite particles.

Thus right from the start, mathematics is inconsistent because the natural numbers themselves are inductively derived from the transfinite recursive composition of a thing that is not isomorphic to any part of existence.  That means mathematics is a formal system of logical deduction based on a false premise. Relative to existence, that means mathematics is logically unsound. In turn, that means it is possible to use "correct" mathematics to derive false conclusions from a true set of premises. In other words, the mathematics may be correct, but the conclusions relative to existence may not be.

We try to compensate for that by comparing the results predicted by mathematics with the observable results from experiments. We then discard, refine, or modify those theories whose mathematical predictions don't match observable reality. The problem with that is observation is anthropocentric. In fact, the very information we use to represent our measurements and observations in terms of is anthropocentric.  Again, let me explain.

Information is Anthropocentric

For all x in the universe, x must exist BEFORE it can be observed, measured, or represented in terms of information. That means existence cannot be composed of information without reversing the order of cause and effect. That means the "It from Bit" hypothesis in quantum physics, that at its deepest levels, existence is composed of information is false, because it requires a reversal of the order of cause and effect.

Information is created by observation and/or measurement of potential differences in energy. Existence is composed of potential differences in energy fields. Existence does not depend on observation or information. Information depends on the existence of energy, and the existence of observers that can measure potential differences in energy fields, and create information to represent them indirectly. In other words, information is an observers' indirect representation of potential differences in energy fields and the relations between them.

Examine the causality graph between energy, existence, observation and information. Existence is composed of, and thus causally depends on, the existence of energy. Observation depends on energy and existence. Information depends on energy, existence, and the observation of both.

Existence is composed of energy, so it is causally dependent on the existence of energy. Everything that exists is composed of some kind of energy. In reality, existence is energy. Thus the dependence between energy and existence is bidirectional.

Observation depends on existence and energy. If there is no existence, there is nothing to observe, no observer to observe it, and no energy for the observer to use to represent anything with. Energy and existence can exist without observation, but observation cannot exist without energy and existence.

Information is dependent on observation, existence and energy. Energy is a potential difference in an energy field. Those potential differences create charge imbalances, and thus disturbances in the energy fields that compose spacetime, matter, and all forces. Those disturbances form travelling waves that propagate through spacetime. Those waves are signals. We interpret those signals as carrying information. More specifically, observers measure the resulting localized potential differences in the energy field that composes a signal when those potential differences cause changes in the receptive field of a sensory transducer, and use the (usually amplified and signal conditioned) potential differences to construct the representation of  information which they then use to represent the associated part of existence indirectly. In other words, once again, I point out that existence is not composed of information. Only our indirect representation of existence is composed of information.

Heisenberg Uncertainty

In fact, the meaning of information, and its reduction in uncertainty is only a reduction in uncertainty relative to the observer that interprets the meaning of the information. The meaning of information, and its uncertainty is in the mind of its interpreter. Of course at quantum scales, the energy required to take a measurement is a substantial fraction of that which composes the localized field being measured, so it changes that field, making subsequent measurements of the same localized field uncertain. Nevertheless, the uncertainty is part of the information we use to represent existence, not part of the energy that composes existence itself. Physical existence itself has no uncertainty. No representation that is complete and consistent in the universal domain can have any uncertainty. Mathematically speaking, uncertainty can only exist in incomplete and/or inconsistent representations. In simple terms, this means information, observation, and measurement are unreliable tools for representing existence, because they are anthropocentric. They are incomplete, inconsistent, and uncertain. As long as physics relies solely on them, it too will remain incomplete, inconsistent, and uncertain.

Direct representation and direct mathematics is not dependent on observation or measurement. In physical form, it generates itself directly from symmetric potential differences in the singularity. It has no undecidability and no uncertainty. Heisenberg Uncertainty is not a fundamental property of physical existence. It is a fundamental property of information. Since we use information to represent all of our observations, we mistakenly attribute the uncertainty in information about existence to existence itself. This isn't difficult to see. The quantity of information in Shannon information theory is mathematically defined in terms of how much it reduces uncertainty. If there is no reduction in uncertainty, the quantity of information is zero. In other words, if there is no reduction in uncertainty, there is no information.

There is a second reason any fixed formal mathematical system is either incomplete or inconsistent. All formal systems are based on information, and information is a kind of indirect representation, in which some observer x, associates some symbol y with some element z to represent z in terms of y indirectly. In any such representation, the symbol y is not the same thing as that which it represents z. In other words, in all indirect representations, y z. That makes it impossible for any indirect representation to be complete and consistent in the universal domain, because it means that nothing that is represented indirectly is itself. In an absolute sense, all indirect representations are inconsistent because they are like a dog chasing its own tail. No fixed formal system based on indirect representation, or any collection of such systems, can ever catch up to itself to represent all of itself completely. Indirect representations can only represent the universal domain incompletely and inconsistently. In other words, information is at best, only an incomplete, partial, inconsistent, uncertain representation of existence. Since numbers are all indirect representations, and since mathematics is based on numbers, mathematics is necessarily incomplete and inconsistent in the universal domain. Of course we already knew that. Kurt Gödel proved as much in his celebrated incompleteness theorems in his 1931 paper entitled "On Formally Undecidable Propositions of Principia Mathematica and Related Systems."

The only possible way all of existence can be complete and consistent is if, for all x in the universe, x = x. The only way that can happen is in the logical converse of an indirect representation: direct representation. In direct representation, everything that exists is composed of energy, and everything that exists contains its own energy. In other words, for all distinct x and y in the universe, the energy that composes x the energy that composes y. Direct representation is the representation of being, not merely information about being. Energy composes everything that physically exists directly, in terms of the potential differences in the energy fields that compose each thing. Those potential differences are the direct representation of direct mathematical relations. Not only do potential differences represent relations, they are energy differences that can cause changes in the things they compose. Hence, they act like mathematical functors. Those functors operate on themselves, transforming their current state into their next state, thereby constructing the current moment of existence throughout all spacetime in the universe. More precisely, potential differences in energy fields are the direct mathematical automorphism group generator generator of physical existence. (No, that "generator generator" isn't a typo). The direct mathematical equations represented by potential differences in energy fulfill all the properties required by the definition of a mathematical group. (I've derived the equations that prove it). Since everything in direct representation represents itself, it is trivially isomorphic to itself. Since there is only one universe, that group can only act on itself, so it has to be an automorphism group.

Physical existence is a self-generated direct mathematical system that generates all of itself directly from the transfinite recursive composition of symmetric potential differences in the singularity. In other words, instead of representing numbers from the transfinite recursive composition of empty-sets, nature represents existence from the transfinite recursive composition of symmetric potential differences in the singularity. In effect, physical existence is a faithful isomorph of the complex number system, except there is no zero. Zero is replaced by the infinite singularity. The infinite singularity acts like an inaccessible cardinal. In addition, nature's equivalent of the complex numbers starts with very large potential differences at each big bang (there are an infinite series of big bangs...), and the magnitude of the potential differences decreases over time as spacetime cools and expands and energy and dark energy compose higher and higher order forms of matter and energy. Eventually, the energy in the quantum vacuum will be exhausted and the expansion of spacetime will slow and then reverse. More and more black holes will form, and space, time and the quantized energy forms will be converted back into their infinite forms, where they will remain trapped in the singularity, until the omega black hole consumes all remaining spacetime in the universe, causing a collapse of its own gravitational field, and the subsequent initiation of the next big bang. Hence, in this model, the universe is an infinite series of big bangs. Between each big bang spacetime undergoes a short period of exponential inflation, followed by a long period of expansion, then an exponential increase in the rate of black hole production near the limit of spacetime expansion resulting in a short period of exponential deflation, followed by a gradually decelerating asymptotic deflation until the omega black hole finally consumes all remaining spacetime in the universe and causes the next big bang.

The result is a symmetrically self-limiting four dimensional pentachoron simplicial complex spacetime lattice composed from a cumulative hierarchy of complex tensor valued quantum energy fields with Gaussian integer coefficients.  (The space between the quantized lattice points is filled by complex and imaginary fractal dimensional non-quantized complex tensor fields with complex real non-integral coefficients that represent the composition of virtual energy and virtual dark energy fractal strings in the quantum vacuum fields). Thus we get time, space, all forms of energy, matter, and complex Hilbert Space tensor hierarchies of quantum field compositions. Time and space both exist physically. Since they both exist, they both must be composed of energy. Spacetime energy field compositions of energy and dark energy compose photons and the elementary particles, and those and their relations compose larger particles and particle systems. We get whole part hierarchies of composition at all spacetime scales above the quantum scale, but because the symmetry of pentachoron simplices is topologically self-dual, the dimension of spacetime never increases beyond the fourth dimension. Instead, as quantum bubbles of temporal energy and anti-temporal dark energy are created via ongoing spontaneous particle pair creation out of the quantum vacuum, it causes the ongoing expansion of four dimensional spacetime. We get time and space, the arrow of time, and the fact that cause precedes effect at all spatial scales above the quantum scale.

Subspace - A New Model of the Quantum Vacuum


Below the quantum scale, spacetime and order break down because virtual energy and virtual dark energy have an imaginary dimensional fractal structure below the quantized unitary imaginary dimension of time, so it has no fixed measure, and time, space, quantum states, and order do not exist. I call the fields that result subspace. Photons and the speed of light are meaningless in subspace. Subspace is filled by the infinite forms of energy. It is infinite because it lacks a measure, not because it is infinite in quantity. Strictly speaking, without a measure, the concept of quantity is undefined and does not exist. Changes can propagate through subspace instantaneously because time and distance have no meaning there. This is what enables the 'spooky action at a distance' observed in entangled quantum systems. It also explains why quantum state changes occur in quantum leaps in zero time.

Physical Existence is Complete and Consistent


Since everything that is itself is consistent with itself, the transfinite recursive composition of everything is also consistent with itself. Thus the universe, and everything that physically exists in it is consistent with itself.

Since the universe is everything that exists, it also has to be complete. That means the universe and everything that physically exists in it is complete and consistent. That means the universe is the union of the finite and the infinite. The quantized forms of energy and dark energy represent the existence of the finite, and the non-quantized forms of energy represent the quantum vacuum, virtual energy, virtual dark energy, and the singularity. In effect, there is a one-to-one isomorphic mapping between the complex field (with the singularity replacing zero), and physical existence. In essence, physical existence itself is a kind of direct mathematical complex number system. The universe as a whole is thus both complete and consistent in the universal domain. The universe is the union of the finite and the infinite, and all relations between them. It is only our indirect representation of existence, based on information, that is incomplete, inconsistent, and uncertain.

The Universe is Finite And Infinite


The universe as a whole is both finite and infinite. In other words, it has finite components and infinite components. Energy comes in finite and infinite forms. Only half of its finite forms are observable. Energy quanta are observable. Dark energy is finite, but unobservable because its arrow of time is reversed. Time and space are finite. All quantized energy forms are finite.

The Solution to the Quantum Vacuum Catastrophe

Virtual energy, virtual dark energy, and the singularity compose the quantum vacuum. Those forms of energy are not quantized, and they are unobservable and unmeasurable. Energy in its infinite forms has no mass or gravitational field. The infinite forms of energy exist beneath and between the quantized dimensions of spacetime. Mass and gravity cannot exist without spacetime. Thus while the singularity and quantum vacuum contain an immense amount of energy, that energy exists in a form that has very little effect on the observable forms of energy. In particular, it has no effect on the cosmological constant. This resolves the so called quantum vacuum catastrophe in quantum physics.

Spontaneous Particle Pair Creation and Annihilation

It is also important to understand that spontaneous particle pair creation and annihilation is a misnomer. In reality, in particle pair creation, virtual energy and virtual dark energy is being transformed from its infinite form into its finite form as energy and dark energy quanta. Thus, those quanta appear spontaneously from the quantum vacuum. The same process works in reverse in particle pair annihilation. In that case, finite energy and dark energy quanta are converted back into their infinite virtual energy and dark virtual energy non-quantized forms. No creation or destruction of energy is involved in this process. It is just another kind of energy transformation. The only thing that makes it appear special is that the energy is being transformed between observable and unobservable forms.

Time and Space are Quantized Energy Forms

Since energy composes everything that exists, and since time and space exist in the universe, time and space must both be composed of energy. Time and space are finite, and they must exist because we can measure them and travel through them. In addition, gravity creates spacetime curvature. It is not possible to create curvature in something that doesn't exist.

The Future of Mathematics and Physics

The only way to represent physics completely and consistently is to use a mathematics that itself is complete and consistent. The only way to do that is to redefine mathematics, and the concept of number in terms of direct representation. Science will never be isomorphic to existence as long it is based on mathematics that isn't.

I am deriving a new foundation for mathematics based on an isomorph of direct representation. The resulting mathematics is both complete and consistent in the universal domain. When completed, in theory it could simulate the generation of the totality of existence, starting from the singularity, completely and consistently. Of course, in reality, resource constraints will make that impossible, but it will still be able to represent many parts of existence that are inaccessible using mathematics represented in terms of indirect representation. For example, we will be able to consistently represent the singularity, We will be able to consistently represent what happens inside black holes. We will be able to consistently represent the complete quantum state of existence consistently, with no uncertainty. We will be able to represent all relations between energy and dark energy. We will be able to represent the quantum vacuum, and all possible relations between it and the finite, observable parts of existence. We will be able to obtain a complete and consistent understanding of the quantum field structure of existence. At least we will have the equations and be able solve them. Admittedly, some of the equations become extremely complex, and it will take quite some time to interpret them and understand all their implications.

11 comments:

  1. Just thought I'd take this opportunity to grab the first comment :-)

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  2. I'm working on the next post on this subject. It will go into a lot more detail about the precise relations between energy, information, observation and existence, and include more detail on the changes I made in the foundation of mathematics to make it complete and consistent in the universal domain.

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  3. I'd like to see some serious theorizing about the origin of the chief characteristics of the macro structures of the cosmos, namely, the galaxies. The big bang theory can't explain their shapes or rotations. It seems to me that the only thing that can explain those features is an origin as the inverse of a black hole whose mass escapes from one dimension into another and does so with a great deal of spin which results in the equatorial centrifugal force that results in not a spherical explosion but a disk-shaped explosion and expansion that rotates. This hypothesis postulates that each galaxy is a universe unto itself and had no connection to the origin of any other galaxy, since each came into being in different times and space. It also postulates that the phenomenon of red-shift observed in the light spectrum, which is the basis of calculations for cosmic distance and speed is not caused by greater speed away from our observation point but due to the presence of dark matter. or powerful gravitation fields. If so, then the whole hypothesis of the big bang dissolves and there was no "beginning" of the universe. Instead, each galaxy had its own beginning and its own age. What is required for this to be so is at least two dimensions, between which massive black holes can explode into the other. As a layman, this theory makes very plausible sense. But my knowledge and imagination ends at this point.
    If there is another good explanation as to why galaxies spin, why they form in the first place as disks if they originate as a blobbish three-dimensional field of hydrogen instead of how they actually end up shape-wise., then I've never heard of such explanation. Adrien Nash

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    1. Hi Adrien,

      I think you are partly correct. The inverse of a black hole is a white hole. A white hole is a time reversed black hole. Instead of consuming energy and matter it produces them. There is recent observational evidence that white holes exist. They may cause some types of quasars. However, white holes are unstable at large scales because the mass they produce creates a large gravitational field that causes them to quickly collapse into black holes. In other words, at large scales, they can only exist for a brief time. However, they might be able to eject enough matter before collapsing into a black hole, so that perhaps that matter could accrete, forming stars and a galaxy around its central black hole.

      However, the part of your theory that I think is incorrect is that galaxies are their own universes. Spacetime exists between the galaxies. Galaxies themselves form larger structures, called galactic clusters in spacetime. Actually, even larger structures than galactic clusters exist.

      In addition, there is only one singularity in the universe. The same singularity exists inside all black holes, and inside every energy and dark energy quantum. It exists beneath the imaginary dimension of time. Consequently, the same singularity can exist everywhere in spacetime. Time and distance have no meaning in the singularity.

      Its also useful to keep in mind that the universe is everything that exists. There can only be one everything. The universe is the union of the finite and the infinite. The idea that multiple universes can exist is logically and mathematically inconsistent.

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  4. Are you familiar with R. Buckminster Fuller's Synergetic Geometry? Like you, he thought that using an incorrect "coordinate system" (e.g., the conventional geometrical system of zero-dimensional "points" lined up into one-dimensional "lines," laid beside each other to form two-dimensional "planes," which are stacked into three-dimensional cubes, the last of which are ostensibly solid, tangible objects built out of three layers of non-existent abstraction) would necessarily lead us astray. Fuller developed a new geometric system based on energetic vectors, with the tetrahedron rather than the cube as the fundamental form. Here is a link to Amy C. Edmundon's book A Fuller Explanation on Google Books.

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    1. Hi kcrady,

      Thanks for the link. It doesn't matter what geometry we develop. Geometry is only an indirect representation of spatial relations. There is far more to existence than geometry, or spatial relations, let alone coordinate systems.

      Existence doesn't depend on coordinate systems. Actually, its far deeper than that. Existence is not causally dependent on observation or information. Things have to exist BEFORE we can observe them or represent them in terms of information. In other words, existence can't be composed of information. That means the logic and mathematics required to represent all of existence cannot be dependent on the representation of information. At best, information is only a partial, incomplete representation of existence. Information is a map of a territory. The map is not the territory. A map is an isomorphic projection. Projections are incomplete. Information is incomplete. That means it is impossible to consistently represent all of existence in terms of information. Information is not primitive enough. Information itself is composed of a lower level representation.

      Our entire view and conception of existence in terms of particles and the relations between them is a neural construct. Particles and their relations in spacetime are just neural abstractions of localized potential difference distributions in energy fields. Particles and relations are not the fundamental components of existence. Existence only has one fundamental component: the potential difference. Everything that exists is composed of energy of some kind. All kinds of energy are composed of potential differences. All energy fields, all particles, all forces and all relations are ultimately composed from potential differences. Even the relation between the finite and the infinite is a potential difference. We call that particular potential difference time. That particular potential difference is so large, it causes all finite changes in existence because everything finite that exists is composed (directly or indirectly) from potential differences in temporal energy. Everything that exists in time does so because it contains a temporal energy component. That includes spacetime, and everything finite that exists in spacetime.

      Just because the energy that composes time is unobservable doesn't mean it doesn't exist. It just means our species can't observe it. Existence doesn't depend on what we can or cannot observe. Existence existed long before we did.

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  5. Hi Barry, logically your arguments seem to make sense, do you have any kind of evidence, i.e., experiments or equations to back them up?

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    1. Hi Jackson,

      I have equations and some proposals for experiments. I also have some explanations for currently unexplained astronomical observations. I am working on an e-book that will go into the theory, logic, and mathematics in more detail.

      Longer term, I want to develop a Mathematica e-book that will teach people direct logic and direct mathematics, and provide a working system with live-equations they can use to generate their own quantum field equations, experiment with the parameters, and plot the results.

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  6. Excellent, is there somewhere you can point me to for more information? In the meantime I'll be eagerly awaiting future publications from you.

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  7. Please note that you should replace the word 'singularity' with 'quantum vacuum', or better yet 'subspace', everywhere it occurs in this post. The reason is that the singularity does not exist in base one mathematics. Base one mathematics is all based on the axiom of identity. Therefore, zero and equality do not exist in base one mathematics. As a result, division by zero is impossible, and the generation of singularities is impossible. Every tensor in base one mathematics is a self-adjoint, complex, symmetric potential difference hyperfunction that operates over a complex tensor field. Those hyperfunctions each contain a derivative and its inverse integral. Composition of those symmetric potential difference hyperfunctions automatically generates successive higher order derivatives and integrals. In quantized form, all symmetric potential differences are othorgonal. In quantized form, those derivatives and integral always exist, up to and including C infinite order. Time itself is the first quantization of the infinite quantum vacuum, and the basis of the unit of the finite. Thus the finite is a symmetric potential difference in the infinite while the infinite is an asymmetric potential difference in the finite. The dot product of each symmetric potential difference tensor with itself is an identity matrix. Hence every symmetric potential difference is an identity. The transfinite recursive composition of those symmetric potential difference identities generates a base one number system, and the quantum field stucture of existence. No identity can be zero (the null matrix is impossible to generate), so no equality and no singularity can exist in the universe. However, non-quantized, asymmetric open virtual energy strings can exist. They compose the 'infinite' fractal quantum vacuum. Actually, the term 'quantum vacuum' is a misnomer. The virtual energy that composes it is neither quantized, nor a vacuum. It should really be called 'subspace' because it fills the fractal dimensional 'space' between the three real dimensions of space and beneath the imaginary dimension of time. Please note that 'infinite' does not mean infinite in quantity. The 'infinite' has no fixed measure. It has a finite quantity, but that quantity is indefinite due to its existence in fractal dimensions. Quantum entanglement occurs in subspace, not the integral dimensions of spacetime, so entangled systems are entangled beneath and between the dimensions of time and space, thereby making them non-local in both time and space, and thus accounting for the "spooky action at a distance" characteristic of entangled quantum systems.

    Sorry for the advanced math braindump, but perhaps, it will help those with advanced mathematical backgrounds understand the foundation of base one mathematics a little better.

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